Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void O_o() {
  ios::sync_with_stdio(0);
  ios_base::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);
}
int main() {
  O_o();
  vector<long long> vec;
  long long l = 1, m = 1;
  while (m < 1000090000) {
    m = (l * (l + 1)) / 2;
    vec.push_back(m);
    l++;
  }
  long long n;
  while (cin >> n) {
    bool in = 0;
    for (int i = 0; i < int(((int)(vec.size()))); i++) {
      if (binary_search(vec.begin(), vec.end(), (n - vec[i]))) {
        in = 1;
        break;
      }
    }
    (in) ? cout << "YES" << endl : cout << "NO" << endl;
  }
  return 0;
}